I think this is mostly a political strategy. At this point in the negotiations over the debt ceiling, it's hard to see how Congress would have the time needed to make any major changes in the debt reduction proposal. It will be hard enough to reach agreement on $2 trillion without involving Social Security at all. Getting to $4 trillion, writing legislation to change Social Security, etc., would take us past the critical date to get the deal done. So I see this mostly as a bargaining strategy for public consumption. The president is saying not only am I willing to consider larger cuts than the other side, but unlike Republicans who won't agree to equitable tax changes, I am also willing to consider cutting programs that are important to Democrats. In short, he is saying I am being more than reasonable, Republicans are not being reasonable at all.
This does several things. First, it puts pressure on Republicans to include substantial revenue enhancement as a part of the deal. I believe the deal is still likely to be far too tilted toward spending cuts, but this may push a bit at the margin. More generally, it also puts pressure on Republicans more to come to a deal rather than shut down government. They are now more likely to be seen as problematically intransigent over the tax issue.
In addition, the Republicans are unlikely to agree to the revenue enhancement that would be required for the Social Security cuts to be part of the deal. If a deal is struck without any changes to Social Security, relieved Democrats may be more likely to endorse it even if it is inequitably tilted toward spending cuts.
It may even be part of an administration strategy to undermine the deal and place the blame on Republicans. But that's risky. Though I doubt that Republicans will call the president's bluff on this -- their constituents will not allow the tax increases that would be needed -- if they do call his bluff then the president is in trouble with his own party. They won't accept big cuts to Social Security any more than Republicans will accept big increases in tax revenue. The president has tried to sell this as strengthening Social Security, and he may have in mind fairly progressive solutions like means testing the program or raising the payroll cap, but even those changes would be a hard sell to his own party. These types of changes are viewed as the first of many on the way to substantially reducing the program, or, as with means testing, threatening to undermine the political support for the program by reducing the return to those with the most political power. The fact that everyone gets benefits, and that those benefits are linked to income to some degree are seen by many as crucial to the program's political support and long-run viability.
Finally, I should acknowledge that the view that this is all a grand political bluff may be a bit of wishful thinking. As I made clear here, I do not think that cuts in Social Security are the right way to bring the program into balance. The problem is not as bad as many people believe -- e.g. the Bush tax cuts alone are larger than the projected shortfall in the program -- and I would prefer to see the focus on the real long run problem, the one driving all the scary debt projections, the growth in health care costs. I could certainly be wrong, and perhaps the president really does want a grand bargain that "strengthens" Social Security. If so, he's headed for trouble.